Evgenii Dadonov had a goal and two assists, Aleksander Barkov had a goal and an assist , and Troy Brouwer and Nick Bjugstad scored for the Panthers (0-1-1), who were playing their home opener.
James Reimer, starting with Roberto Luongo out with a knee injury, made 27 saves.
"I thought we played well for the most part," Reimer said. "Honestly, a couple of bad bounces. We worked hard and had our chances and they got a couple of lucky ones. That's just the way it goes sometimes."
Columbus tied it 4-4 at 1:15 of the third period when Jenner scored after his shot from the half-boards bounced off the stick of Florida defenseman Keith Yandle.
"We just played more straight-ahead, more north hockey (in the third period)," Blue Jackets coach John Tortorella said. "I'm not going to answer many questions about the second period, but I will say it was probably one of the most stubborn, arrogant periods I've seen this team play as far as [what] they think they can do in the National Hockey League. So I'll leave it at that. We talked very quickly when they came in after the second period and I left it up to them. So I appreciate how they handled themselves. We score kind of a shaky goal, but that was our whole game plan, was trying to get pucks to the net. We find a way."
Columbus took a 2-0 lead in the first period with goals by Werenski and Panarin. Werenski scored at 13:29 on a 5-on-3 power play with a one-timer high to the glove side. Panarin scored at 17:20 on a breakaway after a turnover in the neutral zone.